LMFDB - Embedded newform 33.7.c.a.10.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,7,Mod(10,33)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("33.10");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	33.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.59178475946$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 486x^{10} + 82401x^{8} + 6062364x^{6} + 204706260x^{4} + 2964086784x^{2} + 15081209856 $ x^12 + 486x^10 + 82401x^8 + 6062364x^6 + 204706260x^4 + 2964086784*x^2 + 15081209856
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{11} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			10.6
Root			$-3.61107i$ of defining polynomial
Character	$\chi$	$=$	33.10
Dual form			33.7.c.a.10.7

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.61107i q^{2} +15.5885 q^{3} +50.9602 q^{4} +42.6809 q^{5} -56.2910i q^{6} +392.632i q^{7} -415.129i q^{8} +243.000 q^{9} +O(q^{10})$	\(q-3.61107i q^{2} +15.5885 q^{3} +50.9602 q^{4} +42.6809 q^{5} -56.2910i q^{6} +392.632i q^{7} -415.129i q^{8} +243.000 q^{9} -154.124i q^{10} +(1221.13 + 529.529i) q^{11} +794.390 q^{12} -2614.11i q^{13} +1417.82 q^{14} +665.330 q^{15} +1762.39 q^{16} -7831.12i q^{17} -877.490i q^{18} +9649.74i q^{19} +2175.03 q^{20} +6120.53i q^{21} +(1912.17 - 4409.59i) q^{22} -1967.26 q^{23} -6471.22i q^{24} -13803.3 q^{25} -9439.75 q^{26} +3788.00 q^{27} +20008.6i q^{28} +28825.0i q^{29} -2402.55i q^{30} -31174.9 q^{31} -32932.4i q^{32} +(19035.5 + 8254.54i) q^{33} -28278.7 q^{34} +16757.9i q^{35} +12383.3 q^{36} -71389.1 q^{37} +34845.9 q^{38} -40750.0i q^{39} -17718.1i q^{40} -71814.1i q^{41} +22101.7 q^{42} +103360. i q^{43} +(62229.0 + 26984.9i) q^{44} +10371.5 q^{45} +7103.91i q^{46} +53492.4 q^{47} +27472.9 q^{48} -36511.2 q^{49} +49844.8i q^{50} -122075. i q^{51} -133216. i q^{52} +57810.9 q^{53} -13678.7i q^{54} +(52119.0 + 22600.8i) q^{55} +162993. q^{56} +150425. i q^{57} +104089. q^{58} -128925. q^{59} +33905.3 q^{60} -59098.8i q^{61} +112575. i q^{62} +95409.7i q^{63} -6128.19 q^{64} -111573. i q^{65} +(29807.7 - 68738.7i) q^{66} -208435. q^{67} -399075. i q^{68} -30666.5 q^{69} +60514.0 q^{70} -621842. q^{71} -100876. i q^{72} +125609. i q^{73} +257791. i q^{74} -215173. q^{75} +491752. i q^{76} +(-207910. + 479456. i) q^{77} -147151. q^{78} -46759.6i q^{79} +75220.5 q^{80} +59049.0 q^{81} -259326. q^{82} -496587. i q^{83} +311903. i q^{84} -334240. i q^{85} +373241. q^{86} +449338. i q^{87} +(219823. - 506927. i) q^{88} -166520. q^{89} -37452.1i q^{90} +1.02639e6 q^{91} -100252. q^{92} -485968. q^{93} -193165. i q^{94} +411860. i q^{95} -513365. i q^{96} +1.49652e6 q^{97} +131845. i q^{98} +(296735. + 128675. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 204 q^{4} + 224 q^{5} + 2916 q^{9}+O(q^{10}) $ 12 * q - 204 * q^4 + 224 * q^5 + 2916 * q^9	$ 12 q - 204 q^{4} + 224 q^{5} + 2916 q^{9} - 3464 q^{11} + 1944 q^{12} - 6708 q^{14} + 1944 q^{15} + 5316 q^{16} - 44092 q^{20} + 60468 q^{22} - 15304 q^{23} + 95652 q^{25} - 76020 q^{26} - 58608 q^{31} + 4212 q^{33} + 117768 q^{34} - 49572 q^{36} - 202512 q^{37} + 29208 q^{38} - 264708 q^{42} + 434356 q^{44} + 54432 q^{45} + 516920 q^{47} - 377136 q^{48} + 157812 q^{49} - 1042192 q^{53} + 262656 q^{55} + 463020 q^{56} + 1029432 q^{58} - 461008 q^{59} - 417636 q^{60} - 725364 q^{64} + 200232 q^{66} + 364752 q^{67} + 504144 q^{69} - 1028400 q^{70} - 755176 q^{71} + 1364688 q^{75} - 102384 q^{77} + 1219212 q^{78} - 1220764 q^{80} + 708588 q^{81} - 158688 q^{82} + 248760 q^{86} - 2493252 q^{88} - 3513544 q^{89} - 702768 q^{91} + 6899300 q^{92} + 789264 q^{93} + 2370192 q^{97} - 841752 q^{99}+O(q^{100}) $ 12 * q - 204 * q^4 + 224 * q^5 + 2916 * q^9 - 3464 * q^11 + 1944 * q^12 - 6708 * q^14 + 1944 * q^15 + 5316 * q^16 - 44092 * q^20 + 60468 * q^22 - 15304 * q^23 + 95652 * q^25 - 76020 * q^26 - 58608 * q^31 + 4212 * q^33 + 117768 * q^34 - 49572 * q^36 - 202512 * q^37 + 29208 * q^38 - 264708 * q^42 + 434356 * q^44 + 54432 * q^45 + 516920 * q^47 - 377136 * q^48 + 157812 * q^49 - 1042192 * q^53 + 262656 * q^55 + 463020 * q^56 + 1029432 * q^58 - 461008 * q^59 - 417636 * q^60 - 725364 * q^64 + 200232 * q^66 + 364752 * q^67 + 504144 * q^69 - 1028400 * q^70 - 755176 * q^71 + 1364688 * q^75 - 102384 * q^77 + 1219212 * q^78 - 1220764 * q^80 + 708588 * q^81 - 158688 * q^82 + 248760 * q^86 - 2493252 * q^88 - 3513544 * q^89 - 702768 * q^91 + 6899300 * q^92 + 789264 * q^93 + 2370192 * q^97 - 841752 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	3.61107i		−	0.451384i	−0.974199	−	0.225692i	$-0.927536\pi$
$2$		−	3.61107i		−	0.451384i	0.974199	−	0.225692i	$-0.0724643\pi$
$3$	15.5885			0.577350
$3$	15.5885			0.577350
$4$	50.9602			0.796253
$5$	42.6809			0.341448			0.170724	−	0.985319i	$-0.445389\pi$
$5$	42.6809			0.341448			0.170724	+	0.985319i	$0.445389\pi$
$6$		−	56.2910i		−	0.260607i
$7$			392.632i			1.14470i	0.820009	+	0.572350i	$0.193968\pi$
$7$			392.632i			1.14470i	−0.820009	+	0.572350i	$0.806032\pi$
$8$		−	415.129i		−	0.810799i
$9$	243.000			0.333333
$10$		−	154.124i		−	0.154124i
$11$	1221.13	+	529.529i	0.917454	+	0.397843i
$11$	1221.13	+	529.529i	0.917454	+	0.397843i
$12$	794.390			0.459717
$13$		−	2614.11i		−	1.18986i	−0.803779	−	0.594928i	$-0.797181\pi$
$13$		−	2614.11i		−	1.18986i	0.803779	−	0.594928i	$-0.202819\pi$
$14$	1417.82			0.516699
$15$	665.330			0.197135
$16$	1762.39			0.430271
$17$		−	7831.12i		−	1.59396i	−0.604007	−	0.796979i	$-0.706430\pi$
$17$		−	7831.12i		−	1.59396i	0.604007	−	0.796979i	$-0.293570\pi$
$18$		−	877.490i		−	0.150461i
$19$			9649.74i			1.40687i	0.710758	+	0.703436i	$0.248352\pi$
$19$			9649.74i			1.40687i	−0.710758	+	0.703436i	$0.751648\pi$
$20$	2175.03			0.271879
$21$			6120.53i			0.660893i
$22$	1912.17	−	4409.59i	0.179580	−	0.414124i
$23$	−1967.26			−0.161688			−0.0808440	−	0.996727i	$-0.525762\pi$
$23$	−1967.26			−0.161688			−0.0808440	+	0.996727i	$0.525762\pi$
$24$		−	6471.22i		−	0.468115i
$25$	−13803.3			−0.883414
$26$	−9439.75			−0.537082
$27$	3788.00			0.192450
$28$			20008.6i			0.911471i
$29$			28825.0i			1.18189i	0.806713	+	0.590943i	$0.201244\pi$
$29$			28825.0i			1.18189i	−0.806713	+	0.590943i	$0.798756\pi$
$30$		−	2402.55i		−	0.0889835i
$31$	−31174.9			−1.04645			−0.523226	−	0.852194i	$-0.675272\pi$
$31$	−31174.9			−1.04645			−0.523226	+	0.852194i	$0.675272\pi$
$32$		−	32932.4i		−	1.00502i
$33$	19035.5	+	8254.54i	0.529692	+	0.229695i
$34$	−28278.7			−0.719487
$35$			16757.9i			0.390855i
$36$	12383.3			0.265418
$37$	−71389.1			−1.40938			−0.704688	−	0.709518i	$-0.748913\pi$
$37$	−71389.1			−1.40938			−0.704688	+	0.709518i	$0.748913\pi$
$38$	34845.9			0.635039
$39$		−	40750.0i		−	0.686964i
$40$		−	17718.1i		−	0.276845i
$41$		−	71814.1i		−	1.04198i	−0.853564	−	0.520989i	$-0.825563\pi$
$41$		−	71814.1i		−	1.04198i	0.853564	−	0.520989i	$-0.174437\pi$
$42$	22101.7			0.298317
$43$			103360.i			1.30001i	0.759929	+	0.650007i	$0.225234\pi$
$43$			103360.i			1.30001i	−0.759929	+	0.650007i	$0.774766\pi$
$44$	62229.0	+	26984.9i	0.730525	+	0.316783i
$45$	10371.5			0.113816
$46$			7103.91i			0.0729833i
$47$	53492.4			0.515227			0.257613	−	0.966248i	$-0.417064\pi$
$47$	53492.4			0.515227			0.257613	+	0.966248i	$0.417064\pi$
$48$	27472.9			0.248417
$49$	−36511.2			−0.310340
$50$			49844.8i			0.398759i
$51$		−	122075.i		−	0.920272i
$52$		−	133216.i		−	0.947426i
$53$	57810.9			0.388313			0.194157	−	0.980971i	$-0.437803\pi$
$53$	57810.9			0.388313			0.194157	+	0.980971i	$0.437803\pi$
$54$		−	13678.7i		−	0.0868688i
$55$	52119.0	+	22600.8i	0.313262	+	0.135842i
$56$	162993.			0.928123
$57$			150425.i			0.812258i
$58$	104089.			0.533484
$59$	−128925.			−0.627741			−0.313870	−	0.949466i	$-0.601626\pi$
$59$	−128925.			−0.627741			−0.313870	+	0.949466i	$0.601626\pi$
$60$	33905.3			0.156969
$61$		−	59098.8i		−	0.260369i	−0.991490	−	0.130184i	$-0.958443\pi$
$61$		−	59098.8i		−	0.260369i	0.991490	−	0.130184i	$-0.0415569\pi$
$62$			112575.i			0.472351i
$63$			95409.7i			0.381567i
$64$	−6128.19			−0.0233772
$65$		−	111573.i		−	0.406273i
$66$	29807.7	−	68738.7i	0.103680	−	0.239094i
$67$	−208435.			−0.693020			−0.346510	−	0.938046i	$-0.612633\pi$
$67$	−208435.			−0.693020			−0.346510	+	0.938046i	$0.612633\pi$
$68$		−	399075.i		−	1.26919i
$69$	−30666.5			−0.0933506
$70$	60514.0			0.176426
$71$	−621842.			−1.73742			−0.868710	−	0.495321i	$-0.835050\pi$
$71$	−621842.			−1.73742			−0.868710	+	0.495321i	$0.835050\pi$
$72$		−	100876.i		−	0.270266i
$73$			125609.i			0.322888i	0.986882	+	0.161444i	$0.0516152\pi$
$73$			125609.i			0.322888i	−0.986882	+	0.161444i	$0.948385\pi$
$74$			257791.i			0.636169i
$75$	−215173.			−0.510039
$76$			491752.i			1.12023i
$77$	−207910.	+	479456.i	−0.455411	+	1.05021i
$78$	−147151.			−0.310084
$79$		−	46759.6i		−	0.0948396i	−0.998875	−	0.0474198i	$-0.984900\pi$
$79$		−	46759.6i		−	0.0948396i	0.998875	−	0.0474198i	$-0.0150999\pi$
$80$	75220.5			0.146915
$81$	59049.0			0.111111
$82$	−259326.			−0.470332
$83$		−	496587.i		−	0.868483i	−0.900797	−	0.434241i	$-0.857017\pi$
$83$		−	496587.i		−	0.868483i	0.900797	−	0.434241i	$-0.142983\pi$
$84$			311903.i			0.526238i
$85$		−	334240.i		−	0.544253i
$86$	373241.			0.586805
$87$			449338.i			0.682362i
$88$	219823.	−	506927.i	0.322571	−	0.743871i
$89$	−166520.			−0.236209			−0.118105	−	0.993001i	$-0.537682\pi$
$89$	−166520.			−0.236209			−0.118105	+	0.993001i	$0.537682\pi$
$90$		−	37452.1i		−	0.0513746i
$91$	1.02639e6			1.36203
$92$	−100252.			−0.128745
$93$	−485968.			−0.604169
$94$		−	193165.i		−	0.232565i
$95$			411860.i			0.480373i
$96$		−	513365.i		−	0.580247i
$97$	1.49652e6			1.63971			0.819855	−	0.572571i	$-0.194054\pi$
$97$	1.49652e6			1.63971			0.819855	+	0.572571i	$0.194054\pi$
$98$			131845.i			0.140083i
$99$	296735.	+	128675.i	0.305818	+	0.132614i
$100$	−703420.			−0.703420
$101$			388608.i			0.377179i	0.982056	+	0.188590i	$0.0603916\pi$
$101$			388608.i			0.377179i	−0.982056	+	0.188590i	$0.939608\pi$
$102$	−440822.			−0.415396
$103$	1.38871e6			1.27087			0.635434	−	0.772156i	$-0.280821\pi$
$103$	1.38871e6			1.27087			0.635434	+	0.772156i	$0.280821\pi$
$104$	−1.08519e6			−0.964734
$105$			261230.i			0.225660i
$106$		−	208759.i		−	0.175278i
$107$		−	1.05288e6i		−	0.859461i	−0.902957	−	0.429730i	$-0.858609\pi$
$107$		−	1.05288e6i		−	0.859461i	0.902957	−	0.429730i	$-0.141391\pi$
$108$	193037.			0.153239
$109$		−	2.23766e6i		−	1.72789i	−0.503590	−	0.863943i	$-0.667988\pi$
$109$		−	2.23766e6i		−	1.72789i	0.503590	−	0.863943i	$-0.332012\pi$
$110$	81613.0	−	188205.i	0.0613171	−	0.141402i
$111$	−1.11285e6			−0.813703
$112$			691972.i			0.492532i
$113$	576068.			0.399244			0.199622	−	0.979873i	$-0.436029\pi$
$113$	576068.			0.399244			0.199622	+	0.979873i	$0.436029\pi$
$114$	543194.			0.366640
$115$	−83964.4			−0.0552080
$116$			1.46893e6i			0.941080i
$117$		−	635230.i		−	0.396619i
$118$			465556.i			0.283352i
$119$	3.07475e6			1.82461
$120$		−	276198.i		−	0.159837i
$121$	1.21076e6	+	1.29325e6i	0.683442	+	0.730005i
$122$	−213410.			−0.117526
$123$		−	1.11947e6i		−	0.601586i
$124$	−1.58868e6			−0.833240
$125$	−1.25603e6			−0.643087
$126$	344531.			0.172233
$127$		−	69435.1i		−	0.0338975i	−0.999856	−	0.0169488i	$-0.994605\pi$
$127$		−	69435.1i		−	0.0338975i	0.999856	−	0.0169488i	$-0.00539522\pi$
$128$		−	2.08554e6i		−	0.994465i
$129$			1.61123e6i			0.750563i
$130$	−402897.			−0.183385
$131$			2.62760e6i			1.16881i	0.811461	+	0.584407i	$0.198673\pi$
$131$			2.62760e6i			1.16881i	−0.811461	+	0.584407i	$0.801327\pi$
$132$	970055.	+	420653.i	0.421769	+	0.182895i
$133$	−3.78880e6			−1.61045
$134$			752673.i			0.312818i
$135$	161675.			0.0657116
$136$	−3.25093e6			−1.29238
$137$	−3.87616e6			−1.50744			−0.753720	−	0.657196i	$-0.771743\pi$
$137$	−3.87616e6			−1.50744			−0.753720	+	0.657196i	$0.771743\pi$
$138$			110739.i			0.0421370i
$139$			777361.i			0.289453i	0.989472	+	0.144727i	$0.0462303\pi$
$139$			777361.i			0.289453i	−0.989472	+	0.144727i	$0.953770\pi$
$140$			853987.i			0.311220i
$141$	833864.			0.297466
$142$			2.24551e6i			0.784243i
$143$	1.38425e6	−	3.19217e6i	0.473376	−	1.09164i
$144$	428261.			0.143424
$145$			1.23028e6i			0.403552i
$146$	453583.			0.145747
$147$	−569153.			−0.179175
$148$	−3.63800e6			−1.12222
$149$		−	1.16258e6i		−	0.351450i	−0.984439	−	0.175725i	$-0.943773\pi$
$149$		−	1.16258e6i		−	0.351450i	0.984439	−	0.175725i	$-0.0562270\pi$
$150$			777004.i			0.230223i
$151$		−	754146.i		−	0.219041i	−0.993985	−	0.109520i	$-0.965069\pi$
$151$		−	754146.i		−	0.219041i	0.993985	−	0.109520i	$-0.0349315\pi$
$152$	4.00589e6			1.14069
$153$		−	1.90296e6i		−	0.531320i
$154$	1.73135e6	+	750778.i	0.474048	+	0.205565i
$155$	−1.33057e6			−0.357308
$156$		−	2.07663e6i		−	0.546997i
$157$	1.64892e6			0.426089			0.213044	−	0.977043i	$-0.431662\pi$
$157$	1.64892e6			0.426089			0.213044	+	0.977043i	$0.431662\pi$
$158$	−168852.			−0.0428091
$159$	901183.			0.224193
$160$		−	1.40559e6i		−	0.343160i
$161$		−	772409.i		−	0.185084i
$162$		−	213230.i		−	0.0501538i
$163$	5.90835e6			1.36428			0.682140	−	0.731221i	$-0.261049\pi$
$163$	5.90835e6			1.36428			0.682140	+	0.731221i	$0.261049\pi$
$164$		−	3.65966e6i		−	0.829677i
$165$	812455.	+	352311.i	0.180862	+	0.0784287i
$166$	−1.79321e6			−0.392019
$167$		−	2.85288e6i		−	0.612540i	−0.951945	−	0.306270i	$-0.900919\pi$
$167$		−	2.85288e6i		−	0.612540i	0.951945	−	0.306270i	$-0.0990810\pi$
$168$	2.54081e6			0.535852
$169$	−2.00678e6			−0.415757
$170$	−1.20696e6			−0.245667
$171$			2.34489e6i			0.468958i
$172$			5.26725e6i			1.03514i
$173$			7.37387e6i			1.42416i	0.702101	+	0.712078i	$0.252246\pi$
$173$			7.37387e6i			1.42416i	−0.702101	+	0.712078i	$0.747754\pi$
$174$	1.62259e6			0.308007
$175$		−	5.41964e6i		−	1.01124i
$176$	2.15211e6	+	933236.i	0.394754	+	0.171180i
$177$	−2.00974e6			−0.362426
$178$			601316.i			0.106621i
$179$	8.93894e6			1.55857			0.779286	−	0.626669i	$-0.215582\pi$
$179$	8.93894e6			1.55857			0.779286	+	0.626669i	$0.215582\pi$
$180$	528532.			0.0906262
$181$	−6.16407e6			−1.03952			−0.519759	−	0.854313i	$-0.673978\pi$
$181$	−6.16407e6			−1.03952			−0.519759	+	0.854313i	$0.673978\pi$
$182$		−	3.70635e6i		−	0.614798i
$183$		−	921259.i		−	0.150324i
$184$			816666.i			0.131097i
$185$	−3.04695e6			−0.481228
$186$			1.75486e6i			0.272712i
$187$	4.14680e6	−	9.56282e6i	0.634145	−	1.46238i
$188$	2.72598e6			0.410251
$189$			1.48729e6i			0.220298i
$190$	1.48726e6			0.216833
$191$	2.10284e6			0.301791			0.150895	−	0.988550i	$-0.451784\pi$
$191$	2.10284e6			0.301791			0.150895	+	0.988550i	$0.451784\pi$
$192$	−95529.0			−0.0134968
$193$			1.22837e7i			1.70867i	0.519722	+	0.854335i	$0.326035\pi$
$193$			1.22837e7i			1.70867i	−0.519722	+	0.854335i	$0.673965\pi$
$194$		−	5.40404e6i		−	0.740138i
$195$		−	1.73925e6i		−	0.234562i
$196$	−1.86062e6			−0.247109
$197$			2.81236e6i			0.367851i	0.982940	+	0.183926i	$0.0588805\pi$
$197$			2.81236e6i			0.367851i	−0.982940	+	0.183926i	$0.941119\pi$
$198$	464656.	−	1.07153e6i	0.0598599	−	0.138041i
$199$	1.17046e6			0.148524			0.0742620	−	0.997239i	$-0.476340\pi$
$199$	1.17046e6			0.148524			0.0742620	+	0.997239i	$0.476340\pi$
$200$			5.73017e6i			0.716271i
$201$	−3.24918e6			−0.400115
$202$	1.40329e6			0.170253
$203$	−1.13176e7			−1.35291
$204$		−	6.22097e6i		−	0.732769i
$205$		−	3.06509e6i		−	0.355781i
$206$		−	5.01473e6i		−	0.573649i
$207$	−478044.			−0.0538960
$208$		−	4.60709e6i		−	0.511961i
$209$	−5.10981e6	+	1.17836e7i	−0.559714	+	1.29074i
$210$	943320.			0.101859
$211$			5.89158e6i			0.627169i	0.949560	+	0.313584i	$0.101530\pi$
$211$			5.89158e6i			0.627169i	−0.949560	+	0.313584i	$0.898470\pi$
$212$	2.94606e6			0.309196
$213$	−9.69355e6			−1.00310
$214$	−3.80201e6			−0.387947
$215$			4.41151e6i			0.443886i
$216$		−	1.57251e6i		−	0.156038i
$217$		−	1.22403e7i		−	1.19787i
$218$	−8.08035e6			−0.779940
$219$			1.95805e6i			0.186420i
$220$	2.65599e6	+	1.15174e6i	0.249436	+	0.108165i
$221$	−2.04714e7			−1.89658
$222$			4.01856e6i			0.367292i
$223$	3.27462e6			0.295288			0.147644	−	0.989041i	$-0.452831\pi$
$223$	3.27462e6			0.295288			0.147644	+	0.989041i	$0.452831\pi$
$224$	1.29303e7			1.15044
$225$	−3.35421e6			−0.294471
$226$		−	2.08022e6i		−	0.180212i
$227$			1.31678e7i			1.12573i	0.826549	+	0.562865i	$0.190301\pi$
$227$			1.31678e7i			1.12573i	−0.826549	+	0.562865i	$0.809699\pi$
$228$			7.66566e6i			0.646763i
$229$	5.16416e6			0.430025			0.215012	−	0.976611i	$-0.431021\pi$
$229$	5.16416e6			0.430025			0.215012	+	0.976611i	$0.431021\pi$
$230$			303201.i			0.0249200i
$231$	−3.24100e6	+	7.47397e6i	−0.262932	+	0.606339i
$232$	1.19661e7			0.958273
$233$		−	2.27164e7i		−	1.79586i	−0.440140	−	0.897929i	$-0.645071\pi$
$233$		−	2.27164e7i		−	1.79586i	0.440140	−	0.897929i	$-0.354929\pi$
$234$	−2.29386e6			−0.179027
$235$	2.28310e6			0.175923
$236$	−6.57003e6			−0.499840
$237$		−	728910.i		−	0.0547557i
$238$		−	1.11031e7i		−	0.823597i
$239$			5.93806e6i			0.434961i	0.976065	+	0.217481i	$0.0697839\pi$
$239$			5.93806e6i			0.434961i	−0.976065	+	0.217481i	$0.930216\pi$
$240$	1.17257e6			0.0848214
$241$			1.46277e7i			1.04502i	0.852632	+	0.522512i	$0.175005\pi$
$241$			1.46277e7i			1.04502i	−0.852632	+	0.522512i	$0.824995\pi$
$242$	4.67001e6	−	4.37214e6i	0.329512	−	0.308495i
$243$	920483.			0.0641500
$244$		−	3.01168e6i		−	0.207319i
$245$	−1.55833e6			−0.105965
$246$	−4.04249e6			−0.271546
$247$	2.52255e7			1.67398
$248$			1.29416e7i			0.848463i
$249$		−	7.74103e6i		−	0.501419i
$250$			4.53561e6i			0.290279i
$251$	644109.			0.0407322			0.0203661	−	0.999793i	$-0.493517\pi$
$251$	644109.			0.0407322			0.0203661	+	0.999793i	$0.493517\pi$
$252$			4.86209e6i			0.303824i
$253$	−2.40228e6	−	1.04172e6i	−0.148341	−	0.0643264i
$254$	−250735.			−0.0153008
$255$		−	5.21028e6i		−	0.314225i
$256$	−7.92325e6			−0.472262
$257$	2.02780e7			1.19461			0.597306	−	0.802014i	$-0.296238\pi$
$257$	2.02780e7			1.19461			0.597306	+	0.802014i	$0.296238\pi$
$258$	5.81825e6			0.338792
$259$		−	2.80297e7i		−	1.61331i
$260$		−	5.68577e6i		−	0.323496i
$261$			7.00448e6i			0.393962i
$262$	9.48845e6			0.527584
$263$		−	2.44256e7i		−	1.34269i	−0.741143	−	0.671347i	$-0.765716\pi$
$263$		−	2.44256e7i		−	1.34269i	0.741143	−	0.671347i	$-0.234284\pi$
$264$	3.42670e6	−	7.90221e6i	0.186236	−	0.429474i
$265$	2.46743e6			0.132589
$266$			1.36816e7i			0.726930i
$267$	−2.59579e6			−0.136375
$268$	−1.06219e7			−0.551819
$269$	1.95567e7			1.00471			0.502354	−	0.864662i	$-0.332468\pi$
$269$	1.95567e7			1.00471			0.502354	+	0.864662i	$0.332468\pi$
$270$		−	583820.i		−	0.0296612i
$271$			2.68300e7i			1.34807i	0.738699	+	0.674036i	$0.235441\pi$
$271$			2.68300e7i			1.34807i	−0.738699	+	0.674036i	$0.764559\pi$
$272$		−	1.38015e7i		−	0.685834i
$273$	1.59998e7			0.786368
$274$			1.39971e7i			0.680434i
$275$	−1.68557e7	−	7.30926e6i	−0.810491	−	0.351460i
$276$	−1.56277e6			−0.0743307
$277$			1.19678e7i			0.563085i	0.959549	+	0.281543i	$0.0908461\pi$
$277$			1.19678e7i			0.563085i	−0.959549	+	0.281543i	$0.909154\pi$
$278$	2.80711e6			0.130655
$279$	−7.57549e6			−0.348817
$280$	6.95670e6			0.316905
$281$		−	2.30733e7i		−	1.03990i	−0.854197	−	0.519949i	$-0.825951\pi$
$281$		−	2.30733e7i		−	1.03990i	0.854197	−	0.519949i	$-0.174049\pi$
$282$		−	3.01114e6i		−	0.134271i
$283$		−	1.80621e7i		−	0.796910i	−0.917188	−	0.398455i	$-0.869546\pi$
$283$		−	1.80621e7i		−	0.796910i	0.917188	−	0.398455i	$-0.130454\pi$
$284$	−3.16892e7			−1.38343
$285$			6.42026e6i			0.277344i
$286$	−1.15272e7	−	4.99862e6i	−0.492747	−	0.213674i
$287$	2.81966e7			1.19275
$288$		−	8.00257e6i		−	0.335006i
$289$	−3.71888e7			−1.54070
$290$	4.44262e6			0.182157
$291$	2.33284e7			0.946687
$292$			6.40106e6i			0.257101i
$293$			2.05729e7i			0.817887i	0.912560	+	0.408944i	$0.134103\pi$
$293$			2.05729e7i			0.817887i	−0.912560	+	0.408944i	$0.865897\pi$
$294$			2.05525e6i			0.0808767i
$295$	−5.50263e6			−0.214340
$296$			2.96357e7i			1.14272i
$297$	4.62564e6	+	2.00585e6i	0.176564	+	0.0765649i
$298$	−4.19815e6			−0.158639
$299$			5.14264e6i			0.192385i
$300$	−1.09652e7			−0.406120
$301$	−4.05825e7			−1.48813
$302$	−2.72327e6			−0.0988714
$303$			6.05780e6i			0.217765i
$304$			1.70066e7i			0.605336i
$305$		−	2.52239e6i		−	0.0889023i
$306$	−6.87173e6			−0.239829
$307$		−	3.04247e7i		−	1.05150i	−0.850638	−	0.525752i	$-0.823784\pi$
$307$		−	3.04247e7i		−	1.05150i	0.850638	−	0.525752i	$-0.176216\pi$
$308$	−1.05951e7	+	2.44331e7i	−0.362622	+	0.836233i
$309$	2.16479e7			0.733735
$310$			4.80479e6i			0.161283i
$311$	−1.85011e7			−0.615057			−0.307529	−	0.951539i	$-0.599502\pi$
$311$	−1.85011e7			−0.615057			−0.307529	+	0.951539i	$0.599502\pi$
$312$	−1.69165e7			−0.556990
$313$	2.65130e7			0.864622			0.432311	−	0.901725i	$-0.357698\pi$
$313$	2.65130e7			0.864622			0.432311	+	0.901725i	$0.357698\pi$
$314$		−	5.95436e6i		−	0.192330i
$315$			4.07217e6i			0.130285i
$316$		−	2.38288e6i		−	0.0755163i
$317$	−1.40507e7			−0.441083			−0.220541	−	0.975378i	$-0.570782\pi$
$317$	−1.40507e7			−0.441083			−0.220541	+	0.975378i	$0.570782\pi$
$318$		−	3.25424e6i		−	0.101197i
$319$	−1.52637e7	+	3.51991e7i	−0.470205	+	1.08433i
$320$	−261557.			−0.00798208
$321$		−	1.64127e7i		−	0.496210i
$322$	−2.78922e6			−0.0835441
$323$	7.55682e7			2.24250
$324$	3.00915e6			0.0884725
$325$			3.60835e7i			1.05113i
$326$		−	2.13355e7i		−	0.615814i
$327$		−	3.48817e7i		−	0.997595i
$328$	−2.98121e7			−0.844835
$329$			2.10028e7i			0.589780i
$330$	1.27222e6	−	2.93383e6i	0.0354014	−	0.0816382i
$331$	−1.12400e7			−0.309944			−0.154972	−	0.987919i	$-0.549529\pi$
$331$	−1.12400e7			−0.309944			−0.154972	+	0.987919i	$0.549529\pi$
$332$		−	2.53062e7i		−	0.691532i
$333$	−1.73475e7			−0.469792
$334$	−1.03020e7			−0.276490
$335$	−8.89619e6			−0.236630
$336$			1.07868e7i			0.284363i
$337$		−	4.44414e7i		−	1.16117i	−0.814198	−	0.580587i	$-0.802823\pi$
$337$		−	4.44414e7i		−	1.16117i	0.814198	−	0.580587i	$-0.197177\pi$
$338$			7.24662e6i			0.187666i
$339$	8.98002e6			0.230504
$340$		−	1.70329e7i		−	0.433363i
$341$	−3.80686e7	−	1.65080e7i	−0.960071	−	0.416323i
$342$	8.46755e6			0.211680
$343$			3.18573e7i			0.789454i
$344$	4.29078e7			1.05405
$345$	−1.30888e6			−0.0318743
$346$	2.66276e7			0.642840
$347$			1.18184e7i			0.282859i	0.989948	+	0.141430i	$0.0451699\pi$
$347$			1.18184e7i			0.282859i	−0.989948	+	0.141430i	$0.954830\pi$
$348$			2.28983e7i			0.543333i
$349$			3.49082e7i			0.821204i	0.911815	+	0.410602i	$0.134681\pi$
$349$			3.49082e7i			0.821204i	−0.911815	+	0.410602i	$0.865319\pi$
$350$	−1.95707e7			−0.456459
$351$		−	9.90225e6i		−	0.228988i
$352$	1.74386e7	−	4.02148e7i	0.399839	−	0.922056i
$353$	5.66732e7			1.28841			0.644204	−	0.764854i	$-0.277189\pi$
$353$	5.66732e7			1.28841			0.644204	+	0.764854i	$0.277189\pi$
$354$			7.25730e6i			0.163593i
$355$	−2.65408e7			−0.593238
$356$	−8.48589e6			−0.188082
$357$	4.79306e7			1.05344
$358$		−	3.22791e7i		−	0.703514i
$359$		−	7.14406e7i		−	1.54405i	−0.635591	−	0.772026i	$-0.719244\pi$
$359$		−	7.14406e7i		−	1.54405i	0.635591	−	0.772026i	$-0.280756\pi$
$360$		−	4.30550e6i		−	0.0922818i
$361$	−4.60716e7			−0.979290
$362$			2.22589e7i			0.469221i
$363$	1.88739e7	+	2.01597e7i	0.394586	+	0.421468i
$364$	5.23048e7			1.08452
$365$			5.36111e6i			0.110249i
$366$	−3.32673e6			−0.0678538
$367$	3.14164e7			0.635562			0.317781	−	0.948164i	$-0.397062\pi$
$367$	3.14164e7			0.635562			0.317781	+	0.948164i	$0.397062\pi$
$368$	−3.46708e6			−0.0695697
$369$		−	1.74508e7i		−	0.347326i
$370$			1.10028e7i			0.217218i
$371$			2.26985e7i			0.444503i
$372$	−2.47650e7			−0.481071
$373$		−	1.93376e7i		−	0.372629i	−0.982490	−	0.186315i	$-0.940346\pi$
$373$		−	1.93376e7i		−	0.372629i	0.982490	−	0.186315i	$-0.0596544\pi$
$374$	−3.45320e7	−	1.49744e7i	−0.660096	−	0.286243i
$375$	−1.95796e7			−0.371286
$376$		−	2.22062e7i		−	0.417745i
$377$	7.53519e7			1.40627
$378$	5.37071e6			0.0994388
$379$	7.25490e7			1.33264			0.666322	−	0.745664i	$-0.267868\pi$
$379$	7.25490e7			1.33264			0.666322	+	0.745664i	$0.267868\pi$
$380$			2.09885e7i			0.382498i
$381$		−	1.08239e6i		−	0.0195708i
$382$		−	7.59350e6i		−	0.136223i
$383$	−9.04639e7			−1.61020			−0.805099	−	0.593141i	$-0.797888\pi$
$383$	−9.04639e7			−1.61020			−0.805099	+	0.593141i	$0.797888\pi$
$384$		−	3.25104e7i		−	0.574154i
$385$	−8.87380e6	+	2.04636e7i	−0.155499	+	0.358592i
$386$	4.43574e7			0.771266
$387$			2.51165e7i			0.433338i
$388$	7.62629e7			1.30562
$389$	5.67122e7			0.963446			0.481723	−	0.876324i	$-0.340011\pi$
$389$	5.67122e7			0.963446			0.481723	+	0.876324i	$0.340011\pi$
$390$	−6.28055e6			−0.105877
$391$			1.54058e7i			0.257724i
$392$			1.51569e7i			0.251624i
$393$			4.09602e7i			0.674815i
$394$	1.01556e7			0.166042
$395$		−	1.99574e6i		−	0.0323827i
$396$	1.51217e7	+	6.55732e6i	0.243508	+	0.105594i
$397$	−1.44438e7			−0.230839			−0.115420	−	0.993317i	$-0.536821\pi$
$397$	−1.44438e7			−0.230839			−0.115420	+	0.993317i	$0.536821\pi$
$398$		−	4.22661e6i		−	0.0670413i
$399$	−5.90615e7			−0.929793
$400$	−2.43269e7			−0.380107
$401$	−1.25622e8			−1.94819			−0.974096	−	0.226135i	$-0.927391\pi$
$401$	−1.25622e8			−1.94819			−0.974096	+	0.226135i	$0.927391\pi$
$402$			1.17330e7i			0.180606i
$403$			8.14946e7i			1.24513i
$404$			1.98035e7i			0.300330i
$405$	2.52027e6			0.0379386
$406$			4.08688e7i			0.610680i
$407$	−8.71754e7	−	3.78026e7i	−1.29304	−	0.560710i
$408$	−5.06769e7			−0.746156
$409$		−	1.17459e8i		−	1.71679i	−0.512989	−	0.858395i	$-0.671462\pi$
$409$		−	1.17459e8i		−	1.71679i	0.512989	−	0.858395i	$-0.328538\pi$
$410$	−1.10683e7			−0.160594
$411$	−6.04234e7			−0.870321
$412$	7.07689e7			1.01193
$413$		−	5.06200e7i		−	0.718575i
$414$			1.72625e6i			0.0243278i
$415$		−	2.11948e7i		−	0.296541i
$416$	−8.60890e7			−1.19583
$417$			1.21179e7i			0.167116i
$418$	4.25514e7	+	1.84519e7i	0.582619	+	0.252646i
$419$	−4.45678e6			−0.0605869			−0.0302935	−	0.999541i	$-0.509644\pi$
$419$	−4.45678e6			−0.0605869			−0.0302935	+	0.999541i	$0.509644\pi$
$420$			1.33123e7i			0.179683i
$421$	−1.16943e8			−1.56722			−0.783609	−	0.621254i	$-0.786623\pi$
$421$	−1.16943e8			−1.56722			−0.783609	+	0.621254i	$0.786623\pi$
$422$	2.12749e7			0.283094
$423$	1.29986e7			0.171742
$424$		−	2.39990e7i		−	0.314844i
$425$			1.08096e8i			1.40812i
$426$			3.50041e7i			0.452783i
$427$	2.32041e7			0.298044
$428$		−	5.36548e7i		−	0.684348i
$429$	2.15783e7	−	4.97611e7i	0.273303	−	0.630257i
$430$	1.59303e7			0.200363
$431$			1.39148e8i			1.73798i	0.494832	+	0.868989i	$0.335230\pi$
$431$			1.39148e8i			1.73798i	−0.494832	+	0.868989i	$0.664770\pi$
$432$	6.67593e6			0.0828057
$433$	5.29762e6			0.0652555			0.0326278	−	0.999468i	$-0.489612\pi$
$433$	5.29762e6			0.0652555			0.0326278	+	0.999468i	$0.489612\pi$
$434$	−4.42004e7			−0.540701
$435$			1.91782e7i			0.232991i
$436$		−	1.14032e8i		−	1.37583i
$437$		−	1.89835e7i		−	0.227474i
$438$	7.07066e6			0.0841468
$439$			1.41881e7i			0.167699i	0.996478	+	0.0838494i	$0.0267215\pi$
$439$			1.41881e7i			0.167699i	−0.996478	+	0.0838494i	$0.973279\pi$
$440$	9.38225e6	−	2.16361e7i	0.110141	−	0.253993i
$441$	−8.87222e6			−0.103447
$442$			7.39238e7i			0.856086i
$443$	−1.04192e7			−0.119845			−0.0599227	−	0.998203i	$-0.519085\pi$
$443$	−1.04192e7			−0.119845			−0.0599227	+	0.998203i	$0.519085\pi$
$444$	−5.67108e7			−0.647913
$445$	−7.10723e6			−0.0806530
$446$		−	1.18249e7i		−	0.133288i
$447$		−	1.81228e7i		−	0.202910i
$448$		−	2.40612e6i		−	0.0267599i
$449$	1.56473e8			1.72863			0.864313	−	0.502954i	$-0.167754\pi$
$449$	1.56473e8			1.72863			0.864313	+	0.502954i	$0.167754\pi$
$450$			1.21123e7i			0.132920i
$451$	3.80276e7	−	8.76944e7i	0.414543	−	0.955966i
$452$	2.93565e7			0.317899
$453$		−	1.17560e7i		−	0.126463i
$454$	4.75497e7			0.508136
$455$	4.38071e7			0.465061
$456$	6.24456e7			0.658578
$457$			9.09811e7i			0.953241i	0.879109	+	0.476621i	$0.158138\pi$
$457$			9.09811e7i			0.953241i	−0.879109	+	0.476621i	$0.841862\pi$
$458$		−	1.86482e7i		−	0.194106i
$459$		−	2.96642e7i		−	0.306757i
$460$	−4.27884e6			−0.0439595
$461$		−	1.27606e8i		−	1.30247i	−0.758877	−	0.651234i	$-0.774252\pi$
$461$		−	1.27606e8i		−	1.30247i	0.758877	−	0.651234i	$-0.225748\pi$
$462$	2.69890e7	+	1.17035e7i	0.273692	+	0.118683i
$463$	−5.14232e7			−0.518103			−0.259052	−	0.965863i	$-0.583410\pi$
$463$	−5.14232e7			−0.518103			−0.259052	+	0.965863i	$0.583410\pi$
$464$			5.08009e7i			0.508531i
$465$	−2.07416e7			−0.206292
$466$	−8.20306e7			−0.810621
$467$	−7.83092e7			−0.768886			−0.384443	−	0.923149i	$-0.625606\pi$
$467$	−7.83092e7			−0.768886			−0.384443	+	0.923149i	$0.625606\pi$
$468$		−	3.23714e7i		−	0.315809i
$469$		−	8.18382e7i		−	0.793301i
$470$		−	8.24445e6i		−	0.0794087i
$471$	2.57041e7			0.246002
$472$			5.35204e7i			0.508972i
$473$	−5.47322e7	+	1.26216e8i	−0.517201	+	1.19270i
$474$	−2.63215e6			−0.0247158
$475$		−	1.33199e8i		−	1.24285i
$476$	1.56690e8			1.45285
$477$	1.40481e7			0.129438
$478$	2.14427e7			0.196335
$479$			1.90168e8i			1.73034i	0.501483	+	0.865168i	$0.332788\pi$
$479$			1.90168e8i			1.73034i	−0.501483	+	0.865168i	$0.667212\pi$
$480$		−	2.19109e7i		−	0.198124i
$481$			1.86619e8i			1.67695i
$482$	5.28218e7			0.471707
$483$		−	1.20407e7i		−	0.106859i
$484$	6.17005e7	+	6.59041e7i	0.544193	+	0.581268i
$485$	6.38728e7			0.559875
$486$		−	3.32393e6i		−	0.0289563i
$487$	−1.64557e8			−1.42472			−0.712360	−	0.701814i	$-0.752374\pi$
$487$	−1.64557e8			−1.42472			−0.712360	+	0.701814i	$0.752374\pi$
$488$	−2.45336e7			−0.211107
$489$	9.21021e7			0.787668
$490$			5.62725e6i			0.0478308i
$491$		−	3.64073e7i		−	0.307570i	−0.988104	−	0.153785i	$-0.950854\pi$
$491$		−	3.64073e7i		−	0.307570i	0.988104	−	0.153785i	$-0.0491464\pi$
$492$		−	5.70485e7i		−	0.479014i
$493$	2.25732e8			1.88388
$494$		−	9.10911e7i		−	0.755605i
$495$	1.26649e7	+	5.49199e6i	0.104421	+	0.0452808i
$496$	−5.49423e7			−0.450258
$497$		−	2.44155e8i		−	1.98883i
$498$	−2.79534e7			−0.226332
$499$	−3.29524e7			−0.265208			−0.132604	−	0.991169i	$-0.542334\pi$
$499$	−3.29524e7			−0.265208			−0.132604	+	0.991169i	$0.542334\pi$
$500$	−6.40075e7			−0.512060
$501$		−	4.44720e7i		−	0.353650i
$502$		−	2.32592e6i		−	0.0183859i
$503$		−	1.33159e8i		−	1.04633i	−0.852232	−	0.523163i	$-0.824752\pi$
$503$		−	1.33159e8i		−	1.04633i	0.852232	−	0.523163i	$-0.175248\pi$
$504$	3.96073e7			0.309374
$505$			1.65862e7i			0.128787i
$506$	−3.76172e6	+	8.67480e6i	−0.0290359	+	0.0669588i
$507$	−3.12826e7			−0.240037
$508$		−	3.53843e6i		−	0.0269910i
$509$	7.59119e7			0.575648			0.287824	−	0.957683i	$-0.407068\pi$
$509$	7.59119e7			0.575648			0.287824	+	0.957683i	$0.407068\pi$
$510$	−1.88147e7			−0.141836
$511$	−4.93182e7			−0.369611
$512$		−	1.04863e8i		−	0.781293i
$513$			3.65532e7i			0.270753i
$514$		−	7.32254e7i		−	0.539228i
$515$	5.92715e7			0.433934
$516$			8.21083e7i			0.597638i
$517$	6.53212e7	+	2.83257e7i	0.472697	+	0.204979i
$518$	−1.01217e8			−0.728223
$519$			1.14947e8i			0.822236i
$520$	−4.63171e7			−0.329406
$521$	2.69695e8			1.90704			0.953522	−	0.301325i	$-0.0974289\pi$
$521$	2.69695e8			1.90704			0.953522	+	0.301325i	$0.0974289\pi$
$522$	2.52937e7			0.177828
$523$		−	1.19680e8i		−	0.836599i	−0.908309	−	0.418300i	$-0.862626\pi$
$523$		−	1.19680e8i		−	0.836599i	0.908309	−	0.418300i	$-0.137374\pi$
$524$			1.33903e8i			0.930671i
$525$		−	8.44838e7i		−	0.583842i
$526$	−8.82024e7			−0.606071
$527$			2.44134e8i			1.66800i
$528$	3.35481e7	+	1.45477e7i	0.227911	+	0.0988309i
$529$	−1.44166e8			−0.973857
$530$		−	8.91005e6i		−	0.0598484i
$531$	−3.13287e7			−0.209247
$532$	−1.93078e8			−1.28232
$533$	−1.87730e8			−1.23980
$534$			9.37358e6i			0.0615576i
$535$		−	4.49377e7i		−	0.293461i
$536$			8.65274e7i			0.561900i
$537$	1.39344e8			0.899842
$538$		−	7.06207e7i		−	0.453509i
$539$	−4.45850e7	−	1.93337e7i	−0.284723	−	0.123467i
$540$	8.23900e6			0.0523230
$541$			3.13440e8i			1.97953i	0.142702	+	0.989766i	$0.454421\pi$
$541$			3.13440e8i			1.97953i	−0.142702	+	0.989766i	$0.545579\pi$
$542$	9.68851e7			0.608498
$543$	−9.60883e7			−0.600166
$544$	−2.57897e8			−1.60195
$545$		−	9.55055e7i		−	0.589982i
$546$		−	5.77763e7i		−	0.354954i
$547$			6.78738e7i			0.414706i	0.978266	+	0.207353i	$0.0664849\pi$
$547$			6.78738e7i			0.414706i	−0.978266	+	0.207353i	$0.933515\pi$
$548$	−1.97530e8			−1.20030
$549$		−	1.43610e7i		−	0.0867896i
$550$	−2.63943e7	+	6.08670e7i	−0.158643	+	0.365842i
$551$	−2.78154e8			−1.66276
$552$			1.27306e7i			0.0756886i
$553$	1.83593e7			0.108563
$554$	4.32165e7			0.254168
$555$	−4.74973e7			−0.277837
$556$			3.96145e7i			0.230478i
$557$		−	2.31870e7i		−	0.134177i	−0.997747	−	0.0670887i	$-0.978629\pi$
$557$		−	2.31870e7i		−	0.134177i	0.997747	−	0.0670887i	$-0.0213710\pi$
$558$			2.73556e7i			0.157450i
$559$	2.70195e8			1.54683
$560$			2.95340e7i			0.168174i
$561$	6.46422e7	−	1.49070e8i	0.366124	−	0.844307i
$562$	−8.33194e7			−0.469393
$563$		−	3.68985e7i		−	0.206768i	−0.994642	−	0.103384i	$-0.967033\pi$
$563$		−	3.68985e7i		−	0.206768i	0.994642	−	0.103384i	$-0.0329671\pi$
$564$	4.24938e7			0.236858
$565$	2.45871e7			0.136321
$566$	−6.52236e7			−0.359712
$567$			2.31846e7i			0.127189i
$568$			2.58145e8i			1.40870i
$569$		−	1.43565e8i		−	0.779310i	−0.920961	−	0.389655i	$-0.872594\pi$
$569$		−	1.43565e8i		−	0.779310i	0.920961	−	0.389655i	$-0.127406\pi$
$570$	2.31840e7			0.125188
$571$			1.14305e8i			0.613983i	0.951712	+	0.306992i	$0.0993223\pi$
$571$			1.14305e8i			0.613983i	−0.951712	+	0.306992i	$0.900678\pi$
$572$	7.05415e7	−	1.62674e8i	0.376927	−	0.869219i
$573$	3.27800e7			0.174239
$574$		−	1.01820e8i		−	0.538389i
$575$	2.71547e7			0.142837
$576$	−1.48915e6			−0.00779239
$577$	−6.71440e7			−0.349526			−0.174763	−	0.984611i	$-0.555916\pi$
$577$	−6.71440e7			−0.349526			−0.174763	+	0.984611i	$0.555916\pi$
$578$			1.34292e8i			0.695449i
$579$			1.91484e8i			0.986501i
$580$			6.26952e7i			0.321329i
$581$	1.94976e8			0.994153
$582$		−	8.42406e7i		−	0.427319i
$583$	7.05947e7	+	3.06126e7i	0.356260	+	0.154488i
$584$	5.21440e7			0.261798
$585$		−	2.71122e7i		−	0.135424i
$586$	7.42903e7			0.369181
$587$	3.05026e8			1.50808			0.754038	−	0.656831i	$-0.228103\pi$
$587$	3.05026e8			1.50808			0.754038	+	0.656831i	$0.228103\pi$
$588$	−2.90042e7			−0.142669
$589$		−	3.00829e8i		−	1.47222i
$590$			1.98704e7i			0.0967498i
$591$			4.38403e7i			0.212379i
$592$	−1.25815e8			−0.606413
$593$			1.36177e7i			0.0653039i	0.999467	+	0.0326520i	$0.0103953\pi$
$593$			1.36177e7i			0.0653039i	−0.999467	+	0.0326520i	$0.989605\pi$
$594$	7.24327e6	−	1.67035e7i	0.0345601	−	0.0796981i
$595$	1.31233e8			0.623007
$596$		−	5.92452e7i		−	0.279843i
$597$	1.82456e7			0.0857504
$598$	1.85704e7			0.0868397
$599$	−3.71071e8			−1.72654			−0.863270	−	0.504742i	$-0.831588\pi$
$599$	−3.71071e8			−1.72654			−0.863270	+	0.504742i	$0.831588\pi$
$600$			8.93245e7i			0.413539i
$601$		−	1.84279e8i		−	0.848893i	−0.905453	−	0.424447i	$-0.860469\pi$
$601$		−	1.84279e8i		−	0.848893i	0.905453	−	0.424447i	$-0.139531\pi$
$602$			1.46546e8i			0.671716i
$603$	−5.06496e7			−0.231007
$604$		−	3.84314e7i		−	0.174412i
$605$	5.16764e7	+	5.51970e7i	0.233360	+	0.249258i
$606$	2.18752e7			0.0982954
$607$		−	2.82620e8i		−	1.26368i	−0.775099	−	0.631840i	$-0.782300\pi$
$607$		−	2.82620e8i		−	1.26368i	0.775099	−	0.631840i	$-0.217700\pi$
$608$	3.17789e8			1.41393
$609$	−1.76425e8			−0.781101
$610$	−9.10853e6			−0.0401290
$611$		−	1.39835e8i		−	0.613045i
$612$		−	9.69753e7i		−	0.423065i
$613$		−	2.84654e8i		−	1.23576i	−0.786271	−	0.617881i	$-0.787991\pi$
$613$		−	2.84654e8i		−	1.23576i	0.786271	−	0.617881i	$-0.212009\pi$
$614$	−1.09866e8			−0.474632
$615$		−	4.77801e7i		−	0.205410i
$616$	1.99036e8	+	8.63096e7i	0.851510	+	0.369247i
$617$	−1.06481e8			−0.453333			−0.226667	−	0.973972i	$-0.572783\pi$
$617$	−1.06481e8			−0.453333			−0.226667	+	0.973972i	$0.572783\pi$
$618$		−	7.81719e7i		−	0.331196i
$619$	1.88575e8			0.795082			0.397541	−	0.917584i	$-0.369864\pi$
$619$	1.88575e8			0.795082			0.397541	+	0.917584i	$0.369864\pi$
$620$	−6.78062e7			−0.284508
$621$	−7.45196e6			−0.0311169
$622$			6.68086e7i			0.277627i
$623$		−	6.53812e7i		−	0.270389i
$624$		−	7.18174e7i		−	0.295581i
$625$	1.62069e8			0.663833
$626$		−	9.57404e7i		−	0.390276i
$627$	−7.96541e7	+	1.83688e8i	−0.323151	+	0.745209i
$628$	8.40291e7			0.339274
$629$			5.59056e8i			2.24649i
$630$	1.47049e7			0.0588086
$631$	1.34867e8			0.536808			0.268404	−	0.963306i	$-0.413504\pi$
$631$	1.34867e8			0.536808			0.268404	+	0.963306i	$0.413504\pi$
$632$	−1.94113e7			−0.0768959
$633$			9.18407e7i			0.362096i
$634$			5.07380e7i			0.199098i
$635$		−	2.96356e6i		−	0.0115742i
$636$	4.59245e7			0.178514
$637$			9.54445e7i			0.369260i
$638$	1.27107e8	+	5.51182e7i	0.489447	+	0.212243i
$639$	−1.51108e8			−0.579140
$640$		−	8.90130e7i		−	0.339557i
$641$	−3.95961e7			−0.150341			−0.0751706	−	0.997171i	$-0.523950\pi$
$641$	−3.95961e7			−0.150341			−0.0751706	+	0.997171i	$0.523950\pi$
$642$	−5.92675e7			−0.223981
$643$	3.78341e8			1.42315			0.711574	−	0.702611i	$-0.247983\pi$
$643$	3.78341e8			1.42315			0.711574	+	0.702611i	$0.247983\pi$
$644$		−	3.93621e7i		−	0.147374i
$645$			6.87686e7i			0.256278i
$646$		−	2.72882e8i		−	1.01223i
$647$	−1.84845e8			−0.682489			−0.341244	−	0.939975i	$-0.610848\pi$
$647$	−1.84845e8			−0.682489			−0.341244	+	0.939975i	$0.610848\pi$
$648$		−	2.45130e7i		−	0.0900888i
$649$	−1.57434e8	−	6.82693e7i	−0.575923	−	0.249742i
$650$	1.30300e8			0.474465
$651$		−	1.90807e8i		−	0.691593i
$652$	3.01091e8			1.08631
$653$	−7.00273e6			−0.0251494			−0.0125747	−	0.999921i	$-0.504003\pi$
$653$	−7.00273e6			−0.0251494			−0.0125747	+	0.999921i	$0.504003\pi$
$654$	−1.25960e8			−0.450298
$655$			1.12148e8i			0.399089i
$656$		−	1.26565e8i		−	0.448333i
$657$			3.05230e7i			0.107629i
$658$	7.58427e7			0.266217
$659$			1.17604e8i			0.410926i	0.978665	+	0.205463i	$0.0658701\pi$
$659$			1.17604e8i			0.410926i	−0.978665	+	0.205463i	$0.934130\pi$
$660$	4.14028e7	+	1.79538e7i	0.144012	+	0.0624490i
$661$	1.87371e7			0.0648780			0.0324390	−	0.999474i	$-0.489673\pi$
$661$	1.87371e7			0.0648780			0.0324390	+	0.999474i	$0.489673\pi$
$662$			4.05885e7i			0.139904i
$663$	−3.19118e8			−1.09499
$664$	−2.06148e8			−0.704165
$665$	−1.61710e8			−0.549884
$666$			6.26432e7i			0.212056i
$667$		−	5.67063e7i		−	0.191097i
$668$		−	1.45383e8i		−	0.487736i
$669$	5.10462e7			0.170485
$670$			3.21248e7i			0.106811i
$671$	3.12945e7	−	7.21673e7i	0.103586	−	0.238876i
$672$	2.01564e8			0.664209
$673$			4.98061e7i			0.163394i	0.996657	+	0.0816972i	$0.0260340\pi$
$673$			4.98061e7i			0.163394i	−0.996657	+	0.0816972i	$0.973966\pi$
$674$	−1.60481e8			−0.524135
$675$	−5.22870e7			−0.170013
$676$	−1.02266e8			−0.331048
$677$			2.66241e7i			0.0858042i	0.999079	+	0.0429021i	$0.0136603\pi$
$677$			2.66241e7i			0.0858042i	−0.999079	+	0.0429021i	$0.986340\pi$
$678$		−	3.24275e7i		−	0.104046i
$679$			5.87582e8i			1.87698i
$680$	−1.38753e8			−0.441280
$681$			2.05265e8i			0.649940i
$682$	−5.96115e7	+	1.37468e8i	−0.187922	+	0.433361i
$683$	−5.89350e8			−1.84974			−0.924872	−	0.380280i	$-0.875828\pi$
$683$	−5.89350e8			−1.84974			−0.924872	+	0.380280i	$0.875828\pi$
$684$			1.19496e8i			0.373409i
$685$	−1.65438e8			−0.514712
$686$	1.15039e8			0.356347
$687$	8.05013e7			0.248275
$688$			1.82161e8i			0.559358i
$689$		−	1.51124e8i		−	0.462037i
$690$			4.72644e6i			0.0143876i
$691$	2.80860e8			0.851249			0.425624	−	0.904900i	$-0.360055\pi$
$691$	2.80860e8			0.851249			0.425624	+	0.904900i	$0.360055\pi$
$692$			3.75774e8i			1.13399i
$693$	−5.05222e7	+	1.16508e8i	−0.151804	+	0.350070i
$694$	4.26771e7			0.127678
$695$			3.31785e7i			0.0988331i
$696$	1.86533e8			0.553259
$697$	−5.62385e8			−1.66087
$698$	1.26056e8			0.370678
$699$		−	3.54114e8i		−	1.03684i
$700$		−	2.76186e8i		−	0.805206i
$701$			7.39893e7i			0.214790i	0.994216	+	0.107395i	$0.0342510\pi$
$701$			7.39893e7i			0.214790i	−0.994216	+	0.107395i	$0.965749\pi$
$702$	−3.57577e7			−0.103361
$703$		−	6.88886e8i		−	1.98281i
$704$	−7.48332e6	−	3.24505e6i	−0.0214475	−	0.00930044i
$705$	3.55901e7			0.101569
$706$		−	2.04651e8i		−	0.581566i
$707$	−1.52580e8			−0.431758
$708$	−1.02417e8			−0.288583
$709$	−1.29620e8			−0.363692			−0.181846	−	0.983327i	$-0.558207\pi$
$709$	−1.29620e8			−0.363692			−0.181846	+	0.983327i	$0.558207\pi$
$710$			9.58407e7i			0.267778i
$711$		−	1.13626e7i		−	0.0316132i
$712$			6.91274e7i			0.191518i
$713$	6.13290e7			0.169199
$714$		−	1.73081e8i		−	0.475504i
$715$	5.90810e7	−	1.36245e8i	0.161633	−	0.372737i
$716$	4.55530e8			1.24102
$717$			9.25652e7i			0.251125i
$718$	−2.57977e8			−0.696960
$719$	−3.60761e8			−0.970584			−0.485292	−	0.874352i	$-0.661287\pi$
$719$	−3.60761e8			−0.970584			−0.485292	+	0.874352i	$0.661287\pi$
$720$	1.82786e7			0.0489717
$721$			5.45253e8i			1.45476i
$722$			1.66368e8i			0.442036i
$723$			2.28024e8i			0.603344i
$724$	−3.14122e8			−0.827719
$725$		−	3.97882e8i		−	1.04409i
$726$	7.27982e7	−	6.81549e7i	0.190244	−	0.178110i
$727$	−1.89540e8			−0.493283			−0.246642	−	0.969107i	$-0.579327\pi$
$727$	−1.89540e8			−0.493283			−0.246642	+	0.969107i	$0.579327\pi$
$728$		−	4.26083e8i		−	1.10433i
$729$	1.43489e7			0.0370370
$730$	1.93594e7			0.0497648
$731$	8.09426e8			2.07217
$732$		−	4.69475e7i		−	0.119696i
$733$			5.02402e8i			1.27567i	0.770172	+	0.637836i	$0.220170\pi$
$733$			5.02402e8i			1.27567i	−0.770172	+	0.637836i	$0.779830\pi$
$734$		−	1.13447e8i		−	0.286882i
$735$	−2.42920e7			−0.0611789
$736$			6.47865e7i			0.162499i
$737$	−2.54526e8	−	1.10372e8i	−0.635814	−	0.275713i
$738$	−6.30162e7			−0.156777
$739$			2.51962e8i			0.624313i	0.950031	+	0.312156i	$0.101051\pi$
$739$			2.51962e8i			0.624313i	−0.950031	+	0.312156i	$0.898949\pi$
$740$	−1.55273e8			−0.383179
$741$	3.93227e8			0.966470
$742$	8.19657e7			0.200641
$743$			8.18382e7i			0.199522i	0.995011	+	0.0997608i	$0.0318078\pi$
$743$			8.18382e7i			0.199522i	−0.995011	+	0.0997608i	$0.968192\pi$
$744$			2.01739e8i			0.489860i
$745$		−	4.96200e7i		−	0.120002i
$746$	−6.98296e7			−0.168199
$747$		−	1.20671e8i		−	0.289494i
$748$	2.11322e8	−	4.87323e8i	0.504940	−	1.16443i
$749$	4.13393e8			0.983825
$750$			7.07032e7i			0.167593i
$751$	2.39068e7			0.0564418			0.0282209	−	0.999602i	$-0.491016\pi$
$751$	2.39068e7			0.0564418			0.0282209	+	0.999602i	$0.491016\pi$
$752$	9.42744e7			0.221687
$753$	1.00407e7			0.0235168
$754$		−	2.72101e8i		−	0.634769i
$755$		−	3.21877e7i		−	0.0747909i
$756$			7.57925e7i			0.175413i
$757$	−3.57334e8			−0.823734			−0.411867	−	0.911244i	$-0.635123\pi$
$757$	−3.57334e8			−0.823734			−0.411867	+	0.911244i	$0.635123\pi$
$758$		−	2.61980e8i		−	0.601534i
$759$	−3.74478e7	−	1.62388e7i	−0.0856449	−	0.0371389i
$760$	1.70975e8			0.389486
$761$		−	1.50141e8i		−	0.340679i	−0.985385	−	0.170340i	$-0.945514\pi$
$761$		−	1.50141e8i		−	0.340679i	0.985385	−	0.170340i	$-0.0544865\pi$
$762$	−3.90857e6			−0.00883392
$763$	8.78579e8			1.97791
$764$	1.07161e8			0.240302
$765$		−	8.12202e7i		−	0.181418i
$766$			3.26672e8i			0.726817i
$767$			3.37024e8i			0.746921i
$768$	−1.23511e8			−0.272661
$769$			4.67226e8i			1.02742i	0.857964	+	0.513710i	$0.171729\pi$
$769$			4.67226e8i			1.02742i	−0.857964	+	0.513710i	$0.828271\pi$
$770$	7.38955e7	+	3.20439e7i	0.161862	+	0.0701897i
$771$	3.16103e8			0.689709
$772$			6.25981e8i			1.36053i
$773$	−4.23105e8			−0.916030			−0.458015	−	0.888944i	$-0.651439\pi$
$773$	−4.23105e8			−0.916030			−0.458015	+	0.888944i	$0.651439\pi$
$774$	9.06975e7			0.195602
$775$	4.30317e8			0.924450
$776$		−	6.21249e8i		−	1.32948i
$777$		−	4.36939e8i		−	0.931447i
$778$		−	2.04792e8i		−	0.434884i
$779$	6.92988e8			1.46593
$780$		−	8.86324e7i		−	0.186771i
$781$	−7.59350e8	−	3.29283e8i	−1.59400	−	0.691220i
$782$	5.56315e7			0.116332
$783$			1.09189e8i			0.227454i
$784$	−6.43470e7			−0.133530
$785$	7.03774e7			0.145487
$786$	1.47910e8			0.304601
$787$		−	3.79153e8i		−	0.777840i	−0.921272	−	0.388920i	$-0.872848\pi$
$787$		−	3.79153e8i		−	0.777840i	0.921272	−	0.388920i	$-0.127152\pi$
$788$			1.43318e8i			0.292902i
$789$		−	3.80757e8i		−	0.775205i
$790$	−7.20677e6			−0.0146170
$791$			2.26183e8i			0.457015i
$792$	5.34170e7	−	1.23183e8i	0.107524	−	0.247957i
$793$	−1.54491e8			−0.309801
$794$			5.21575e7i			0.104197i
$795$	3.84634e7			0.0765501
$796$	5.96468e7			0.118263
$797$	5.49249e8			1.08491			0.542456	−	0.840084i	$-0.317495\pi$
$797$	5.49249e8			1.08491			0.542456	+	0.840084i	$0.317495\pi$
$798$			2.13275e8i			0.419693i
$799$		−	4.18905e8i		−	0.821250i
$800$			4.54577e8i			0.887845i
$801$	−4.04644e7			−0.0787364
$802$			4.53629e8i			0.879382i
$803$	−6.65136e7	+	1.53385e8i	−0.128459	+	0.296235i
$804$	−1.65579e8			−0.318593
$805$		−	3.29672e7i		−	0.0631966i
$806$	2.94283e8			0.562030
$807$	3.04859e8			0.580068
$808$	1.61323e8			0.305817
$809$			7.06598e8i			1.33453i	0.744823	+	0.667263i	$0.232534\pi$
$809$			7.06598e8i			1.33453i	−0.744823	+	0.667263i	$0.767466\pi$
$810$		−	9.10086e6i		−	0.0171249i
$811$		−	6.37206e8i		−	1.19458i	−0.802024	−	0.597292i	$-0.796243\pi$
$811$		−	6.37206e8i		−	1.19458i	0.802024	−	0.597292i	$-0.203757\pi$
$812$	−5.76749e8			−1.07726
$813$			4.18239e8i			0.778310i
$814$	−1.36508e8	+	3.14797e8i	−0.253095	+	0.583656i
$815$	2.52174e8			0.465830
$816$		−	2.15144e8i		−	0.395967i
$817$	−9.97398e8			−1.82895
$818$	−4.24154e8			−0.774931
$819$	2.49412e8			0.454010
$820$		−	1.56198e8i		−	0.283291i
$821$		−	3.09686e8i		−	0.559619i	−0.960056	−	0.279810i	$-0.909729\pi$
$821$		−	3.09686e8i		−	0.559619i	0.960056	−	0.279810i	$-0.0902713\pi$
$822$			2.18193e8i			0.392849i
$823$	−8.83266e8			−1.58450			−0.792250	−	0.610197i	$-0.791090\pi$
$823$	−8.83266e8			−1.58450			−0.792250	+	0.610197i	$0.791090\pi$
$824$		−	5.76494e8i		−	1.03042i
$825$	−2.62754e8	−	1.13940e8i	−0.467937	−	0.202915i
$826$	−1.82792e8			−0.324353
$827$		−	7.78472e8i		−	1.37634i	−0.725548	−	0.688172i	$-0.758414\pi$
$827$		−	7.78472e8i		−	1.37634i	0.725548	−	0.688172i	$-0.241586\pi$
$828$	−2.43612e7			−0.0429148
$829$	2.06091e7			0.0361739			0.0180870	−	0.999836i	$-0.494242\pi$
$829$	2.06091e7			0.0361739			0.0180870	+	0.999836i	$0.494242\pi$
$830$	−7.65359e7			−0.133854
$831$			1.86559e8i			0.325097i
$832$			1.60198e7i			0.0278155i
$833$			2.85924e8i			0.494669i
$834$	4.37585e7			0.0754334
$835$		−	1.21764e8i		−	0.209150i
$836$	−2.60397e8	+	6.00494e8i	−0.445674	+	1.02776i
$837$	−1.18090e8			−0.201390
$838$			1.60937e7i			0.0273480i
$839$	−1.07054e7			−0.0181266			−0.00906329	−	0.999959i	$-0.502885\pi$
$839$	−1.07054e7			−0.0181266			−0.00906329	+	0.999959i	$0.502885\pi$
$840$	1.08444e8			0.182965
$841$	−2.36059e8			−0.396855
$842$			4.22291e8i			0.707417i
$843$		−	3.59677e8i		−	0.600386i
$844$			3.00236e8i			0.499385i
$845$	−8.56513e7			−0.141959
$846$		−	4.69390e7i		−	0.0775216i
$847$	−5.07771e8	+	4.75384e8i	−0.835637	+	0.782337i
$848$	1.01885e8			0.167080
$849$		−	2.81561e8i		−	0.460096i
$850$	3.90341e8			0.635605
$851$	1.40441e8			0.227879
$852$	−4.93985e8			−0.798721
$853$			4.47111e8i			0.720391i	0.932877	+	0.360196i	$0.117290\pi$
$853$			4.47111e8i			0.720391i	−0.932877	+	0.360196i	$0.882710\pi$
$854$		−	8.37916e7i		−	0.134532i
$855$			1.00082e8i			0.160124i
$856$	−4.37080e8			−0.696850
$857$		−	3.75055e8i		−	0.595871i	−0.954586	−	0.297936i	$-0.903702\pi$
$857$		−	3.75055e8i		−	0.595871i	0.954586	−	0.297936i	$-0.0962981\pi$
$858$	−1.79691e8	−	7.79207e7i	−0.284488	−	0.123365i
$859$	7.15774e8			1.12927			0.564633	−	0.825342i	$-0.309018\pi$
$859$	7.15774e8			1.12927			0.564633	+	0.825342i	$0.309018\pi$
$860$			2.24811e8i			0.353446i
$861$	4.39541e8			0.688636
$862$	5.02472e8			0.784495
$863$	1.23113e8			0.191545			0.0957724	−	0.995403i	$-0.469468\pi$
$863$	1.23113e8			0.191545			0.0957724	+	0.995403i	$0.469468\pi$
$864$		−	1.24748e8i		−	0.193416i
$865$			3.14724e8i			0.486274i
$866$		−	1.91301e7i		−	0.0294553i
$867$	−5.79717e8			−0.889526
$868$		−	6.23766e8i		−	0.953811i
$869$	2.47606e7	−	5.70996e7i	0.0377312	−	0.0870109i
$870$	6.92537e7			0.105168
$871$			5.44872e8i			0.824594i
$872$	−9.28919e8			−1.40097
$873$	3.63654e8			0.546570
$874$	−6.85508e7			−0.102678
$875$		−	4.93158e8i		−	0.736142i
$876$			9.97827e7i			0.148437i
$877$		−	3.70674e7i		−	0.0549532i	−0.999622	−	0.0274766i	$-0.991253\pi$
$877$		−	3.70674e7i		−	0.0549532i	0.999622	−	0.0274766i	$-0.00874718\pi$
$878$	5.12341e7			0.0756965
$879$			3.20700e8i			0.472208i
$880$	9.18540e7	+	3.98314e7i	0.134788	+	0.0584491i
$881$	3.68641e8			0.539108			0.269554	−	0.962985i	$-0.413124\pi$
$881$	3.68641e8			0.539108			0.269554	+	0.962985i	$0.413124\pi$
$882$			3.20382e7i			0.0466942i
$883$	7.49054e8			1.08801			0.544003	−	0.839084i	$-0.316908\pi$
$883$	7.49054e8			1.08801			0.544003	+	0.839084i	$0.316908\pi$
$884$	−1.04323e9			−1.51016
$885$	−8.57775e7			−0.123750
$886$			3.76243e7i			0.0540963i
$887$			5.61810e8i			0.805042i	0.915411	+	0.402521i	$0.131866\pi$
$887$			5.61810e8i			0.805042i	−0.915411	+	0.402521i	$0.868134\pi$
$888$			4.61975e8i			0.659750i
$889$	2.72625e7			0.0388025
$890$			2.56647e7i			0.0364055i
$891$	7.21066e7	+	3.12681e7i	0.101939	+	0.0442047i
$892$	1.66875e8			0.235124
$893$			5.16187e8i			0.724858i
$894$	−6.54427e7			−0.0915902
$895$	3.81522e8			0.532170
$896$	8.18852e8			1.13836
$897$			8.01658e7i			0.111074i
$898$		−	5.65036e8i		−	0.780274i
$899$		−	8.98616e8i		−	1.23679i
$900$	−1.70931e8			−0.234473
$901$		−	4.52724e8i		−	0.618956i
$902$	−3.16671e8	−	1.37320e8i	−0.431508	−	0.187118i
$903$	−6.32619e8			−0.859170
$904$		−	2.39143e8i		−	0.323707i
$905$	−2.63088e8			−0.354941
$906$	−4.24516e7			−0.0570834
$907$	4.89658e8			0.656252			0.328126	−	0.944634i	$-0.393583\pi$
$907$	4.89658e8			0.656252			0.328126	+	0.944634i	$0.393583\pi$
$908$			6.71031e8i			0.896365i
$909$			9.44318e7i			0.125726i
$910$		−	1.58191e8i		−	0.209921i
$911$	2.68430e8			0.355039			0.177519	−	0.984117i	$-0.443193\pi$
$911$	2.68430e8			0.355039			0.177519	+	0.984117i	$0.443193\pi$
$912$			2.65107e8i			0.349491i
$913$	2.62957e8	−	6.06398e8i	0.345520	−	0.796793i
$914$	3.28539e8			0.430278
$915$		−	3.93202e7i		−	0.0513278i
$916$	2.63167e8			0.342408
$917$	−1.03168e9			−1.33794
$918$	−1.07120e8			−0.138465
$919$		−	7.88532e7i		−	0.101595i	−0.998709	−	0.0507975i	$-0.983824\pi$
$919$		−	7.88532e7i		−	0.101595i	0.998709	−	0.0507975i	$-0.0161763\pi$
$920$			3.48561e7i			0.0447626i
$921$		−	4.74274e8i		−	0.607087i
$922$	−4.60793e8			−0.587913
$923$			1.62556e9i			2.06728i
$924$	−1.65162e8	+	3.80875e8i	−0.209360	+	0.482799i
$925$	9.85408e8			1.24506
$926$			1.85693e8i			0.233863i
$927$	3.37457e8			0.423622
$928$	9.49277e8			1.18782
$929$	5.51288e8			0.687592			0.343796	−	0.939044i	$-0.388287\pi$
$929$	5.51288e8			0.687592			0.343796	+	0.939044i	$0.388287\pi$
$930$			7.48992e7i			0.0931169i
$931$		−	3.52324e8i		−	0.436609i
$932$		−	1.15763e9i		−	1.42996i
$933$	−2.88403e8			−0.355103
$934$			2.82780e8i			0.347063i
$935$	1.76989e8	−	4.08150e8i	0.216527	−	0.499327i
$936$	−2.63702e8			−0.321578
$937$			8.86109e7i			0.107713i	0.998549	+	0.0538565i	$0.0171514\pi$
$937$			8.86109e7i			0.107713i	−0.998549	+	0.0538565i	$0.982849\pi$
$938$	−2.95524e8			−0.358083
$939$	4.13297e8			0.499190
$940$	1.16347e8			0.140079
$941$		−	1.59607e9i		−	1.91551i	−0.287593	−	0.957753i	$-0.592855\pi$
$941$		−	1.59607e9i		−	1.91551i	0.287593	−	0.957753i	$-0.407145\pi$
$942$		−	9.28192e7i		−	0.111041i
$943$			1.41277e8i			0.168475i
$944$	−2.27216e8			−0.270099
$945$			6.34789e7i			0.0752201i
$946$	4.55776e8	+	1.97642e8i	0.538366	+	0.233456i
$947$	2.03142e8			0.239194			0.119597	−	0.992823i	$-0.461840\pi$
$947$	2.03142e8			0.239194			0.119597	+	0.992823i	$0.461840\pi$
$948$		−	3.71454e7i		−	0.0435993i
$949$	3.28356e8			0.384191
$950$	−4.80989e8			−0.561002
$951$	−2.19029e8			−0.254659
$952$		−	1.27642e9i		−	1.47939i
$953$			8.22302e8i			0.950064i	0.879969	+	0.475032i	$0.157563\pi$
$953$			8.22302e8i			0.950064i	−0.879969	+	0.475032i	$0.842437\pi$
$954$		−	5.07285e7i		−	0.0584261i
$955$	8.97512e7			0.103046
$956$			3.02604e8i			0.346339i
$957$	−2.37937e8	+	5.48700e8i	−0.271473	+	0.626036i
$958$	6.86709e8			0.781045
$959$		−	1.52191e9i		−	1.72557i
$960$	−4.07727e6			−0.00460845
$961$	8.43677e7			0.0950618
$962$	6.73895e8			0.756950
$963$		−	2.55849e8i		−	0.286487i
$964$			7.45432e8i			0.832103i
$965$			5.24281e8i			0.583421i
$966$	−4.34797e7			−0.0482342
$967$		−	5.79203e8i		−	0.640548i	−0.947325	−	0.320274i	$-0.896225\pi$
$967$		−	5.79203e8i		−	0.640548i	0.947325	−	0.320274i	$-0.103775\pi$
$968$	5.36865e8	−	5.02622e8i	0.591887	−	0.554135i
$969$	1.17799e9			1.29471
$970$		−	2.30649e8i		−	0.252718i
$971$	−1.98740e8			−0.217083			−0.108542	−	0.994092i	$-0.534618\pi$
$971$	−1.98740e8			−0.217083			−0.108542	+	0.994092i	$0.534618\pi$
$972$	4.69080e7			0.0510796
$973$	−3.05217e8			−0.331337
$974$			5.94227e8i			0.643096i
$975$			5.62486e8i			0.606873i
$976$		−	1.04155e8i		−	0.112029i
$977$	4.74752e8			0.509076			0.254538	−	0.967063i	$-0.418077\pi$
$977$	4.74752e8			0.509076			0.254538	+	0.967063i	$0.418077\pi$
$978$		−	3.32587e8i		−	0.355540i
$979$	−2.03343e8	−	8.81772e7i	−0.216711	−	0.0939741i
$980$	−7.94129e7			−0.0843748
$981$		−	5.43752e8i		−	0.575962i
$982$	−1.31469e8			−0.138832
$983$	−1.33343e9			−1.40381			−0.701905	−	0.712271i	$-0.747667\pi$
$983$	−1.33343e9			−1.40381			−0.701905	+	0.712271i	$0.747667\pi$
$984$	−4.64725e8			−0.487766
$985$			1.20034e8i			0.125602i
$986$		−	8.15135e8i		−	0.850352i
$987$			3.27402e8i			0.340510i
$988$	1.28550e9			1.33291
$989$		−	2.03336e8i		−	0.210197i
$990$	1.98320e7	−	4.57339e7i	0.0204390	−	0.0471338i
$991$	−1.40010e9			−1.43859			−0.719296	−	0.694704i	$-0.755535\pi$
$991$	−1.40010e9			−1.43859			−0.719296	+	0.694704i	$0.755535\pi$
$992$			1.02666e9i			1.05170i
$993$	−1.75214e8			−0.178946
$994$	−8.81662e8			−0.897724
$995$	4.99563e7			0.0507132
$996$		−	3.94484e8i		−	0.399256i
$997$			1.54181e9i			1.55577i	0.628406	+	0.777885i	$0.283707\pi$
$997$			1.54181e9i			1.55577i	−0.628406	+	0.777885i	$0.716293\pi$
$998$			1.18994e8i			0.119710i
$999$	−2.70421e8			−0.271234

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.7.c.a.10.6	✓	12
3.2	odd	2		99.7.c.d.10.7		12
4.3	odd	2		528.7.j.c.241.3		12
11.10	odd	2	inner	33.7.c.a.10.7	yes	12
33.32	even	2		99.7.c.d.10.6		12
44.43	even	2		528.7.j.c.241.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.7.c.a.10.6	✓	12	1.1	even	1	trivial
33.7.c.a.10.7	yes	12	11.10	odd	2	inner
99.7.c.d.10.6		12	33.32	even	2
99.7.c.d.10.7		12	3.2	odd	2
528.7.j.c.241.3		12	4.3	odd	2
528.7.j.c.241.4		12	44.43	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	33.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-3.61107i q^{2} +15.5885 q^{3} +50.9602 q^{4} +42.6809 q^{5} -56.2910i q^{6} +392.632i q^{7} -415.129i q^{8} +243.000 q^{9} +O(q^{10})\)	\(q-3.61107i q^{2} +15.5885 q^{3} +50.9602 q^{4} +42.6809 q^{5} -56.2910i q^{6} +392.632i q^{7} -415.129i q^{8} +243.000 q^{9} -154.124i q^{10} +(1221.13 + 529.529i) q^{11} +794.390 q^{12} -2614.11i q^{13} +1417.82 q^{14} +665.330 q^{15} +1762.39 q^{16} -7831.12i q^{17} -877.490i q^{18} +9649.74i q^{19} +2175.03 q^{20} +6120.53i q^{21} +(1912.17 - 4409.59i) q^{22} -1967.26 q^{23} -6471.22i q^{24} -13803.3 q^{25} -9439.75 q^{26} +3788.00 q^{27} +20008.6i q^{28} +28825.0i q^{29} -2402.55i q^{30} -31174.9 q^{31} -32932.4i q^{32} +(19035.5 + 8254.54i) q^{33} -28278.7 q^{34} +16757.9i q^{35} +12383.3 q^{36} -71389.1 q^{37} +34845.9 q^{38} -40750.0i q^{39} -17718.1i q^{40} -71814.1i q^{41} +22101.7 q^{42} +103360. i q^{43} +(62229.0 + 26984.9i) q^{44} +10371.5 q^{45} +7103.91i q^{46} +53492.4 q^{47} +27472.9 q^{48} -36511.2 q^{49} +49844.8i q^{50} -122075. i q^{51} -133216. i q^{52} +57810.9 q^{53} -13678.7i q^{54} +(52119.0 + 22600.8i) q^{55} +162993. q^{56} +150425. i q^{57} +104089. q^{58} -128925. q^{59} +33905.3 q^{60} -59098.8i q^{61} +112575. i q^{62} +95409.7i q^{63} -6128.19 q^{64} -111573. i q^{65} +(29807.7 - 68738.7i) q^{66} -208435. q^{67} -399075. i q^{68} -30666.5 q^{69} +60514.0 q^{70} -621842. q^{71} -100876. i q^{72} +125609. i q^{73} +257791. i q^{74} -215173. q^{75} +491752. i q^{76} +(-207910. + 479456. i) q^{77} -147151. q^{78} -46759.6i q^{79} +75220.5 q^{80} +59049.0 q^{81} -259326. q^{82} -496587. i q^{83} +311903. i q^{84} -334240. i q^{85} +373241. q^{86} +449338. i q^{87} +(219823. - 506927. i) q^{88} -166520. q^{89} -37452.1i q^{90} +1.02639e6 q^{91} -100252. q^{92} -485968. q^{93} -193165. i q^{94} +411860. i q^{95} -513365. i q^{96} +1.49652e6 q^{97} +131845. i q^{98} +(296735. + 128675. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 204 q^{4} + 224 q^{5} + 2916 q^{9}+O(q^{10}) \) 12 * q - 204 * q^4 + 224 * q^5 + 2916 * q^9	\( 12 q - 204 q^{4} + 224 q^{5} + 2916 q^{9} - 3464 q^{11} + 1944 q^{12} - 6708 q^{14} + 1944 q^{15} + 5316 q^{16} - 44092 q^{20} + 60468 q^{22} - 15304 q^{23} + 95652 q^{25} - 76020 q^{26} - 58608 q^{31} + 4212 q^{33} + 117768 q^{34} - 49572 q^{36} - 202512 q^{37} + 29208 q^{38} - 264708 q^{42} + 434356 q^{44} + 54432 q^{45} + 516920 q^{47} - 377136 q^{48} + 157812 q^{49} - 1042192 q^{53} + 262656 q^{55} + 463020 q^{56} + 1029432 q^{58} - 461008 q^{59} - 417636 q^{60} - 725364 q^{64} + 200232 q^{66} + 364752 q^{67} + 504144 q^{69} - 1028400 q^{70} - 755176 q^{71} + 1364688 q^{75} - 102384 q^{77} + 1219212 q^{78} - 1220764 q^{80} + 708588 q^{81} - 158688 q^{82} + 248760 q^{86} - 2493252 q^{88} - 3513544 q^{89} - 702768 q^{91} + 6899300 q^{92} + 789264 q^{93} + 2370192 q^{97} - 841752 q^{99}+O(q^{100}) \) 12 * q - 204 * q^4 + 224 * q^5 + 2916 * q^9 - 3464 * q^11 + 1944 * q^12 - 6708 * q^14 + 1944 * q^15 + 5316 * q^16 - 44092 * q^20 + 60468 * q^22 - 15304 * q^23 + 95652 * q^25 - 76020 * q^26 - 58608 * q^31 + 4212 * q^33 + 117768 * q^34 - 49572 * q^36 - 202512 * q^37 + 29208 * q^38 - 264708 * q^42 + 434356 * q^44 + 54432 * q^45 + 516920 * q^47 - 377136 * q^48 + 157812 * q^49 - 1042192 * q^53 + 262656 * q^55 + 463020 * q^56 + 1029432 * q^58 - 461008 * q^59 - 417636 * q^60 - 725364 * q^64 + 200232 * q^66 + 364752 * q^67 + 504144 * q^69 - 1028400 * q^70 - 755176 * q^71 + 1364688 * q^75 - 102384 * q^77 + 1219212 * q^78 - 1220764 * q^80 + 708588 * q^81 - 158688 * q^82 + 248760 * q^86 - 2493252 * q^88 - 3513544 * q^89 - 702768 * q^91 + 6899300 * q^92 + 789264 * q^93 + 2370192 * q^97 - 841752 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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